Shiyun had some pencils, files and staplers. The ratio of the number of pencils to the number of files was 7 : 1. After giving away 18 files, the ratio of the number of staplers to the number of files was 5 : 1. Shiyun bought another 152 staplers. As a result, there were an equal number of pencils and staplers. How many pencils did she have at first?
| |
Pencils |
Files |
Staplers |
| Before |
7 u |
1 u |
|
| Change |
|
- 18 |
|
| After 1 |
|
1 u - 18 |
5 u - 90 |
| Change |
|
|
+ 152 |
| After 2 |
7 u |
1 u - 18 |
5 u + 62 |
Number of files after Shiyun gave away 18 files
= 1 u - 18
After Shiyun gave away 18 files, the ratio of the number of staplers to the number of files became 5 : 1. This means that the number of files was 5 times as many as the number of staplers.
Number of staplers after Shiyun gave away 18 files
= 5 x (1 u - 18)
= 5 u - 90
Number of staplers in the end after Shiyun bought another 152 staplers
= 5 u - 90 + 152
= 5 u + 62
Number of pencils and staplers in the end is the same.
7 u = 5 u + 627 u - 5 u = 622 u = 62
1 u = 62 ÷ 2 = 31
Total numbers of pencils that Shiyun had at first
= 7 u
= 7 x 31
= 217
Answer(s): 217
